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A . Borsch-Supan Journal of Public Economics 78 2000 25 –49
Table 1. All this suggests that it is worthwhile to conduct a more formal analysis of early retirement incentives.
5. Econometric estimation of disincentive effects: data and methodology
We take up the example of Germany where an econometric analysis is facilitated by the homogeneity of the retirement income provision as described in
Section 2. The methodology follows the seminal work by Stock and Wise 1990. Earlier analyses of the German pension system using this framework were carried
¨ ¨
out by Borsch-Supan 1992, Schmidt 1995, Borsch-Supan and Schmidt 1996, and Siddiqui 1997. We improve on this work by exploiting more systematically
the cross-sectional and time-series variation contained in the 1984–1996 German Socio-Economic Panel GSOEP that spans several modifications of the German
pension system. This section has three parts. We will first describe the data, then the option value framework, and finally our panel data estimation procedure.
5.1. Data The German Socio-Economic Panel GSOEP is an annual panel study of some
5
6000 households and some 15,000 individuals. The design of the GSOEP closely corresponds to the U.S. Panel Study of Income Dynamics PSID. The panel
started in 1984; 13 waves through 1996 are currently available. The GSOEP data provide a detailed account of income and employment status. We constructed an
unbalanced panel of all persons aged 55 through 70 in West Germany for which
6
earnings data is available. This panel includes 1639 individuals with 8474 observations. Average observation time is slightly more than 5 years. The panel is
left-censored as we include only persons who have worked at least 1 year during our window in order to reconstruct an earning history. There is only little right
censoring due to missing interviews. Of the 1639 individuals, 678 have no transitions, 609 have a single transition from employment to retirement, and 352
individuals have more complex histories with at least one reverse transition. Most of these reverse transitions include retirees who pick up part-time work after
7
receiving pension benefits. 35 of our sample persons are female, and the most frequent retirement age is age 60.
5
See Burkhauser 1991 for an English language description.
6
We excluded East Germany because retirement patterns in the East are dominated by the transition ¨
problems to a market economy. See Borsch-Supan and Schmidt 1996 for a comparison.
7
There are no earnings tests for public pension recipients after age 65.
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. Borsch-Supan Journal of Public Economics 78 2000 25 –49 37
5.2. The option value model In order to capture the economic incentives provided by the pension system, we
employ the option value to postpone retirement Stock and Wise, 1990. This value expresses for each retirement age the trade-off between retiring now
resulting in a stream of retirement benefits that depends on this retirement age and keeping all options open for some later retirement date with associated
streams of first labor, then retirement incomes for all possible later retirement ages.
The option value function is closely related to the pension wealth accrual function developed in Section 2 but adds utility from consumption and leisure to
the purely financial incentives analyzed in Section 2. Let V R denote the expected
t
discounted future utility at age t if the worker retires at age R, specified as follows:
R21 `
NET s 2t
s 2t
V R 5
O
uYLAB ? a ?
d 1
a
O
uYRET R ? a ? d
t s
s s
s s 5t
s 5R
with
NET
YLAB after-tax labor income at age s, s 5 t . . . R 2 1
s
YRET R pension income at age s, s . R
s
R retirement age
a marginal utility of leisure, to be estimated
a probability to survive at least until age s
d discount factor51 11r.
Utility from consumption is represented by an isoelastic utility function in
g.
after-tax income, uY 5Y Remember that pension income in Germany is
effectively untaxed. To capture utility from leisure, utility during retirement is weighted by
a .1, where 1 a is the marginal disutility of work. The option value for a specific age is defined as the difference between the
maximum attainable consumption utility if the worker postpones retirement to some later year minus the utility of consumption that the worker can afford if the
worker would retire now. Let Rt denote the optimal retirement age if the worker postpones retirement past age t, i.e., maxV r for r .t. With this notation, the
t
option value is Gt 5 V R t 2 V t .
t t
Since a worker is likely to retire as soon as the utility of the option to postpone retirement becomes smaller than the utility of retiring now, retirement probabilities
should depend negatively on the option value. The option value captures the economic incentives created by the pension
¨ 38
A . Borsch-Supan Journal of Public Economics 78 2000 25 –49
system and the labor market because the retirement income YRET R depends on
s
retirement age according to the adjustment factors in Fig. 3 and on previous labor income by the benefit rules summarized in Section 2. The option value is also
closely linked to the pension accrual that was the focus of Section 2. This is most
8
easily seen in a simple two-period comparison and for g 51. In this crude
approximation, a worker of age R in the first period will retire early if
NET
a ? WR . YLAB 1
a ? WR 1 1 where Wt denotes the present discounted value of pension benefits when retiring
NET
at age t . Using the definition TAXRR5 2[WR112WR] YLAB
from Section 2, it follows that a worker will retire in the first period if TAXRR.1
a. Estimates for
a are between 2.5 and 4 in Germany, see Fig. 7 below. Hence, according to this crude approximation, the tax rates well above 50 exerted by the
current public pension system in Germany will lead to early retirement. We compute the option value for every person in our sample, using the
applicable pension regulations and individual earning histories. Additional private pension income is ignored because it represents only a very small proportion of
retirement income as described before.
5.3. Econometric estimation method The variable to be explained is old age labor force status. Because Germany has
very few part-time employees, we model only two states ‘fully in labor force and fully retired’ unlike the competing risk analysis of Sueyoshi 1989. The definition
of ‘retired’ is problematic, although less so in Germany than in other countries for
Fig. 7. Gridsearch over the inverse marginal disutility of work a. Note: based on Model 1.
8
I am grateful to an anonymous referee for pointing this out.
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. Borsch-Supan Journal of Public Economics 78 2000 25 –49 39
the U.S., see Rust, 1990. Retirement definitions commonly employed in the literature include the retirement status self-reported by the respondent, the fact that
there are few work hours, or the receipt of retirement benefits, among other definitions. We use the first concept, and include pre-retirement, mainly financed
by a mixture of unemployment compensation and severance pay, in our definition of retirement.
Our main explanatory variable is the option value described in the previous subsection. The other explanatory variables are the usual suspects: an array of
socio-economic variables such as gender, marital status, wealth indicator vari- ables of several financial and real wealth categories and a self-assessed health
measure. We do not use the legal disability status as a measure of health since this is endogenous to the retirement decision. The desire for early retirement may
prompt workers to seek disability status, and frequently the employer helps in this process to alleviate restructuring. Until recently, disability status was granted for
labor market reasons without a link to health.
We link the explanatory variables to the dependent variable by a panel probit model with a parameterized correlation pattern over time. The model can be
interpreted as a semi-nonparametric hazard model for multiple spell data, permitting unobserved heterogeneity and state dependence without imposing a
9
functional form on the duration in a given state. Inserting the option value in a regression-type model is a practical estimation procedure that generates robust
estimates of the average effects of the option value on retirement, see Lumbsdaine
10
et al. 1992. Nevertheless, discrete choice models for panel data are necessarily computation-
ally involved because the space of possible outcomes is so large, in our case
T
2 58192 choice sequences. Although not all of these choice sequences are observed in our data, there are sufficiently many complex choice sequences in the
data to warrant a departure from a simple one-spell hazard model. We structure the choices by cross-sectional utility maximization
Person n chooses retirement in period t ⇔
u 5 X b 1 ´ . 0
nt nt
nt
where the utility u is the sum of a deterministic utility component which depends
nt
on the vector of observable variables X and a parameter vector b to be estimated,
nt
and a random utility component ´ .
nt
We assume that this random component is normally distributed. The probability of a choice sequence is therefore a T-dimensional normal probability. If utilities
are correlated over time, which is likely in our panel data, these probabilities are difficult to evaluate. Two examples for intertemporal linkages are particular
9
Flexible hazard rate models of retirement have been estimated by Sueyoshi 1989 and Meghir and ¨
Whitehouse 1997, parametric hazard rate models for German data by Schmidt 1995 and Borsch- Supan and Schmidt 1996.
10
The full underlying dynamic programming model has been estimated by Rust and Phelan 1997.
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A . Borsch-Supan Journal of Public Economics 78 2000 25 –49
relevant for our application: random effects and autocorrelation. In the language of duration models, random effects capture unobserved population heterogeneity,
such as a preference for leisure that deviates from the mean. Autocorrelated errors capture elements of state dependency, such as early retirement due to a one-time
health shock. More formally, a random-effect structure is imposed by specifying
2
´ 5 u 1 n for
n i.i.d. and u normally distributed with variance s .
nt n
nt nt
n
An autoregressive error structure can be incorporated as ´ 5 r ? ´
1 n
for n i.i.d. and 0 , r , 1.
nt nt 21
nt nt
Finally, both error structures can be combined by specifying the random utility component as
´ 5 u 1h where h 5 r ?h 1
n for
n i.i.d. and 0 , r , 1.
nt n
nt nt
nt 21 nt
nt
This model can only be identified in reasonably long panels, and formally if T 3. Classical evaluation of the resulting panel-data probit choice probabilities is
computationally infeasible since only random effects can be factorized Moffitt, 1987 and the number of operations increases exponentially with the length of the
panel, T . We instead use the smooth simulated maximum likelihood estimation
¨ SSML method proposed by Borsch-Supan and Hajivassiliou 1993 which
simulates the choice probabilities by drawing pseudo-random realizations from the underlying error process. This algorithm is very quick, depends continuously on
the parameters b and M, and is currently the most efficient method for panel data
11
probit models. This method, as it applies to our application, is sketched in
Appendix A.
6. Econometric estimation of disincentive effects: results
